Efficient computerized calculation of resource reallocation scheduling schemes

Abstract

The present disclosure relates to a computer system comprising a database including, a reallocation scheduling module, the reallocation scheduling module configured to obtain an objective function including one or more integer-valued decision variables and automatically determine a proposed reallocation scheme for each of one or more items between a plurality of locations based on the objective function, wherein determining the reallocation scheme includes finding values of one or more decision variables that optimize the objective function while obeying the one or more constraints, wherein determining a proposed reallocation scheme includes solving an integer quadratic programming problem.

What is claimed is: 
     
       1. A computer system, comprising:
 at least one processor; and 
 a non-transitory computer-readable storage medium coupled to the at least one processor, the storage medium storing a database including information regarding a current stock of each of one or more items in each of a plurality of locations, historical data regarding a rate of decrease of a stock of each of the items in each of the plurality of locations, and historical data regarding replenishments of a stock of each of the items in each of the plurality of locations, the storage medium further storing programming instructions for execution by the at least one processor, the programming instructions instructing the at least one processor to:
 determine average values and deviation values for the rate of decrease of the stock of each of the items in each of the plurality of locations and average values and deviation values for replenishment durations of the stock of each of the items in each of the plurality of locations; 
 obtain an objective function including one or more integer-valued decision variables, a first decision variable indicating a quantity of each of the one or more items to be transported between each of the plurality of locations, wherein one or more terms of the objective function include the first decision variable, the current stock of one or more items in the plurality of locations, and the average values and deviation values of the rate of decrease of the stock of the items in each of the plurality of locations and replenishment durations of the stock of each of the items in each of the plurality of locations, and wherein the objective function is a quadratic function with respect to the one or more decision variables; 
 obtain one or more constraints, wherein the one or more constraints are linear with respect to the one or more decision variables; 
 automatically determine a proposed reallocation scheme for each of the items between the plurality of locations based on the objective function, wherein determining the reallocation scheme includes finding values of one or more decision variables that optimize the objective function while obeying the one or more constraints, wherein determining a proposed reallocation scheme includes solving an integer quadratic programming problem; and 
 automatically determine a required quantity of a particular item at a particular location based on the current stock of the particular item at the particular location and average values and deviation values for the rate of decrease of the stock of the particular item at the particular location and replenishment durations of the stock of the particular item at the particular location, wherein the required quantity of the particular item at the particular location is calculated as a minimum required quantity minus a current stock of the particular item, wherein the minimum required quantity is determined based on an average value of a rate of decrease of the stock of a first item at a second location multiplied with the replenishment duration of the stock of the first item at the second location plus an amount determined based on the deviation of the rate of decrease of the stock of the first item at the second location and a deviation of the replenishment duration of the stock of the first item at the second location; and 
 implementing the determined proposed reallocation scheme for each of the items between the plurality of locations. 
 
 
     
     
       2. The computer system of  claim 1 , wherein the objective function includes a term quantifying a benefit of a transport of a first item of the one or more items from a first location of the plurality of locations to a second location of the plurality of locations, wherein the term quantifying a benefit is determined based on a linear approximation of a nonlinear function determining an incremental benefit per unit of the first item transported from the first location to the second location. 
     
     
       3. The computer system of  claim 2 , wherein the benefit is determined based on a cumulative value calculated based on the linear approximation of a nonlinear function determining an incremental benefit per unit of the first item transported from the first location to the second location. 
     
     
       4. The computer system of  claim 2 , wherein the nonlinear function determining an incremental benefit per unit of the first item includes a first section of constant incremental benefit per unit and a second section with a nonlinearly decreasing incremental benefit per unit. 
     
     
       5. The computer system of  claim 4 , wherein a boundary between the first section and the second section is determined based on an average value of a rate of decrease of a stock of the first item at the second location and based on a replenishment duration of the stock of the first item at the second location. 
     
     
       6. The computer system of  claim 5 , wherein the linear approximation includes approximating the nonlinear function by a linear function, wherein the linear function crosses the nonlinear function at the boundary between the first section and wherein the linear function yields an incremental benefit of zero for a predetermined number of transported items, the predetermined number of items being higher than an average value of the rate of decrease of the stock of the first item at the second location multiplied with the replenishment duration of the stock of the first item at the second location by a predetermined amount. 
     
     
       7. The computer system of  claim 6 , wherein the predetermined amount is determined based on the deviation of the a rate of decrease of the stock of the first item at the second location and a deviation of the replenishment duration of the stock of the first item at the second location. 
     
     
       8. The computer system of  claim 2 , wherein the objective function further includes a term quantifying a cost of a transport of the first item from the first location to the second location of the plurality of locations. 
     
     
       9. The computer system of  claim 8 , wherein the term quantifying the cost is determined based at least on a cost of transport per unit between the first location and the second location and a number of transport vehicles required to transport a particular number of first items from the first location to the second location. 
     
     
       10. The computer system of  claim 1 , wherein a first constraint of the one or more constraints is that a number of items of a first item transported from a first location of the plurality of locations to a second location of the plurality of locations shall not exceed a required quantity of the first item at the second location. 
     
     
       11. The computer system of  claim 9 , wherein a second constraint of the one or more constraints is that a number of items of a first item transported from a first location of the plurality of locations to a second location of the plurality of locations shall not exceed a capacity for the first item at the second location. 
     
     
       12. The computer system of  claim 9 , wherein a third constraint of the one or more constraints is that a number of vehicles required to transport a quantity of first items from a first location of the plurality of locations to a second location of the plurality of locations shall not exceed an available number of vehicles at the first location. 
     
     
       13. The computer system of  claim 1 , wherein determining average values and deviation values for the rate of decrease of the stock of each of the items in each of the plurality of locations and replenishment durations of the stock of each of the items in each of the plurality of locations includes approximating historical data regarding a rate of decrease of a stock of each of the items in each of the plurality of locations and historical data regarding replenishments of a stock of each of the items in each of the plurality of locations by normal distributions. 
     
     
       14. The computer system of  claim 13 , wherein the average values are arithmetic means and the deviation values are standard deviations. 
     
     
       15. The computer system of  claim 1 , wherein terms of the objective function are further determined based on a price of each of the items. 
     
     
       16. A computer-implemented method executed by at least one processor, the method comprising:
 determining, by the at least one processor, average values and deviation values for a rate of decrease of a stock of each item of one or more items in each of a plurality of locations replenishment durations of the stock of each of the items in each of the plurality of locations; 
 obtaining, by the at least one processor, an objective function including one or more integer-valued decision variables, a first decision variable indicating a quantity of each of the one or more items to be transported between each of the plurality of locations, wherein one or more terms of the objective function include the first decision variable, a current stock of one or more items in the plurality of locations, and the average values and deviation values of the rate of decrease of the stock of the items in each of the plurality of locations and replenishment durations of the stock of each of the items in each of the plurality of locations, and wherein the objective function is a quadratic function with respect to the one or more decision variables; 
 obtaining, by the at least one processor, one or more constraints, wherein the one or more constraints are linear with respect to the one or more decision variables; 
 automatically determining, by the at least one processor, a proposed reallocation scheme for each of the items between the plurality of locations based on the objective function, wherein determining the reallocation scheme includes finding values of one or more decision variables that optimize the objective function while obeying the one or more constraints, wherein determining a proposed reallocation scheme includes solving an integer quadratic programming problem, and wherein the objective function includes a term quantifying a benefit of a transport of a first item of the one or more items from a first location of the plurality of locations to a second location of the plurality of locations, wherein the term quantifying a benefit is determined based on a linear approximation of a nonlinear function determining an incremental benefit per unit of the first item transported from the first location to the second location, wherein the nonlinear function determining the incremental benefit per unit of the first item includes a first section of constant incremental benefit per unit and a second section with a nonlinearly decreasing incremental benefit per unit, and wherein a boundary between the first section and the second section is determined based on an average value of a rate of decrease of a stock of the first item at the second location and based on a replenishment duration of the stock of the first item at the second location; and 
 implementing the determined proposed reallocation scheme for each of the items between the plurality of locations. 
 
     
     
       17. A computer-readable medium storing instructions thereon which when executed by at least one processor cause the at least one processor to perform operations comprising:
 determining, by the at least one processor, average values and deviation values for a rate of decrease of a stock of each item of one or more items in each of a plurality of locations replenishment durations of the stock of each of the items in each of the plurality of locations; 
 obtaining, by the at least one processor, an objective function including one or more integer-valued decision variables, a first decision variable indicating a quantity of each of the one or more items to be transported between each of the plurality of locations, wherein one or more terms of the objective function include the first decision variable, the current stock of one or more items in the plurality of locations, and the average values and deviation values of the rate of decrease of the stock of the items in each of the plurality of locations and replenishment durations of the stock of each of the items in each of the plurality of locations, and wherein the objective function is a quadratic function with respect to the one or more decision variables; 
 obtaining, by the at least one processor, one or more constraints, wherein the one or more constraints are linear with respect to the one or more decision variables; 
 automatically determining, by the at least one processor, a proposed reallocation scheme for each of the items between the plurality of locations based on the objective function, wherein determining the reallocation scheme includes finding values of one or more decision variables that optimize the objective function while obeying the one or more constraints, wherein determining a proposed reallocation scheme includes solving an integer quadratic programming problem; and 
 automatically determining, by the at least one processor, a required quantity of a particular item at a particular location based on a current stock of the particular item at the particular location and average values and deviation values for the rate of decrease of the stock of the particular item at the particular location and replenishment durations of the stock of the particular item at the particular location, wherein the required quantity of the particular item at the particular location is calculated as a minimum required quantity minus a current stock of the particular item, wherein the minimum required quantity is determined based on an average value of a rate of decrease of the stock of a first item at a second location multiplied with the replenishment duration of the stock of the first item at the second location plus an amount which is determined based on the deviation of the rate of decrease of the stock of the first item at the second location and a deviation of the replenishment duration of the stock of the first item at the second location; and 
 implementing the determined proposed reallocation scheme for each of the items between the plurality of locations.